expressing a quantity as a constant or coefficient

A quadratic can be written several equivalent ways, and each way makes a different quantity easy to read off.
A quantity shown as a constant or coefficient is one that appears as a plain number in the expression, not something you have to compute.

Factored form, $y = a(x - r_1)(x - r_2)$, shows the x-intercepts directly.
The numbers $r_1$ and $r_2$ are exactly where the parabola crosses the $x$-axis.
For example, $y = (x - 2)(x - 5)$ shows its x-intercepts as $2$ and $5$.

Vertex form, $y = a(x - h)^2 + k$, shows the vertex directly.
The vertex sits at $(h, k)$, right there in the expression.
For example, $y = (x - 1)^2 + 4$ shows its vertex as $(1, 4)$.

Standard form, $y = ax^2 + bx + c$, shows the y-intercept directly.
The constant term $c$ is the value when $x = 0$, which is the y-intercept.
So the last number in standard form is the y-intercept.

So the strategy is simple: decide which quantity the question wants displayed, then choose the matching form.
The right answer is the equivalent form that shows that value as a plain constant or coefficient.

The parabola $y = x^2 + 6x - 16$ has x-intercepts at $2$ and $-8$. Which equivalent form shows these intercepts directly?
The factored form $y = a(x - r_1)(x - r_2)$ puts the x-intercepts where you can read them off.
So $y = (x - 2)(x + 8)$ displays the intercepts $2$ and $-8$.

Which form of a quadratic displays its vertex as constants?
The vertex form $y = a(x - h)^2 + k$ shows the vertex $(h, k)$ directly.
For example, $y = (x + 3)^2 - 25$ displays its vertex as $(-3, -25)$.

Which form of $y = 2x^2 - 8x + 3$ shows its y-intercept as a constant?
The standard form ends in a constant term, which is the value at $x = 0$.
So $y = 2x^2 - 8x + 3$ shows the y-intercept $3$ directly.